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A rectangle is 5.1 cm wide and each diagonal is 9.3 cm long. What is the measure of the angle between a diagonal and the shorter side of the rectangle to the nearest tenth of a degree?

Sagot :

Answer:

56.7°

Step-by-step explanation:

A rectangle is 5.1 cm wide and each diagonal is 9.3 cm long. What is the measure of the angle between a diagonal and the shorter side of the rectangle to the nearest tenth of a degree?

We solve this question using the Trigonometric function of Sine

From the question, we are told that:

A rectangle is 5.1 cm wide

and each diagonal is 9.3 cm long.

Since we have a diagonal, this means the shape is transformed to a triangle.

The width of the rectangle = Adjacent side of a triangle = 5.1cm

The diagonal of the rectangle = Hypotenuse = 9.3cm

Hence,

cosθ = Adjacent/Hypotenuse

cosθ = 5.1/9.3

cosθ = 0.5483870968

θ = arccos(0.5483870968)

θ = 56.743568714°

Approximately = 56.7°

The measure of the angle is 56.7°

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